Econometric Learning Research Articles

Social Learning for the Masses

I consider a plausible role for social learning as implemented in the work of Jasmina Arifovic in a complex macroeconomic environment. The model is DSGE with considerable heterogeneity, enough to approach Gini coefficients for income, wealth, and consumption in the U.S. data. The economy has an ambient stochastic structure, and I consider transition dynamics following exceptionally large shocks like the global financial crisis or the global pandemic. These shocks are large enough to plausibly perturb the economy out of the rational expectations equilibrium associated with more ordinary shocks. How is equilibrium re-established? I argue that a social learning construct may be more appropriate in this environment, as opposed to the econometric learning constructs often used to analyze departures from rational expectations in the literature. I also argue that a “DNA” feature of social learning may have led to relatively fast convergence to rational expectations observed following these large shocks in the U.S. data.

Estimating Case‐based Individual and Social Learning in Corporate Tax Avoidance

AbstractWe build an econometric learning model based on case‐based decision theory to analyse tax avoidance by Chinese manufacturing firms. In our model, firms forecast the consequences of tax avoidance by judging the similarity between present and remembered circumstances. We allow firms to consider not only their own experiences but also those of neighbouring firms. This is the first empirically fitted model of case‐based individual and social learning. Our measure of tax avoidance is based on underreported profits, which we measure using difference‐in‐difference (DID) and propensity score matching (PSM) with a case‐based similarity function between non‐state and state firms. We find that firms learn from their past and neighbours' experiences weighted as about 65% as important as their own. We also find that the average tax audit rate for non‐state firms is less than 2% and that more than half of non‐state firms practice tax avoidance. Our government policy simulations suggest that increasing the tax audit rate or fine would significantly deter tax avoidance.

Sampling properties of the Bayesian posterior mean with an application to WALS estimation

Many statistical and econometric learning methods rely on Bayesian ideas. When applied in a frequentist setting, their precision is often assessed using the posterior variance. This is permissible asymptotically, but not necessarily in finite samples. We explore this issue focusing on weighted-average least squares (WALS), a Bayesian-frequentist ‘fusion’. Exploiting the sampling properties of the posterior mean in the normal location model, we derive estimators of the finite-sample bias and variance of WALS. We study the performance of the proposed estimators in an empirical application and a closely related Monte Carlo experiment which analyze the impact of legalized abortion on crime.

Recent Developments in Factor Models and Applications in Econometric Learning

This article provides a selective overview of the recent developments in factor models and their applications in econometric learning. We focus on the perspective of the low-rank structure of factor models and particularly draw attention to estimating the model from the low-rank recovery point of view. Our survey mainly consists of three parts. The first part is a review of new factor estimations based on modern techniques for recovering low-rank structures of high-dimensional models. The second part discusses statistical inferences of several factor-augmented models and their applications in statistical learning models. The final part summarizes new developments dealing with unbalanced panels from the matrix completion perspective.

Recent Developments on Factor Models and its Applications in Econometric Learning

This paper provides a selective overview on the recent development of factor models and their applications in econometric learning. We focus on the perspective of the low-rank structure of factor models, and particularly draws attentions to estimating the model from the low-rank recovery point of view. The survey mainly consists of three parts: the first part is a review on new factor estimations based on modern techniques on recovering low-rank structures of high-dimensional models. The second part discusses statistical inferences of several factor-augmented models and applications in statistical learning models. The final part summarizes new developments dealing with unbalanced panels from the matrix completion perspective.

Sampling Properties of the Bayesian Posterior Mean With an Application to WALS Estimation

Many statistical and econometric learning methods rely on Bayesian ideas, often applied or reinterpreted in a frequentist setting. Two leading examples are shrinkage estimators and model averaging estimators, such as weighted-average least squares (WALS). In many instances, the accuracy of these learning methods in repeated samples is assessed using the variance of the posterior distribution of the parameters of interest given the data. This may be permissible when the sample size is large because, under the conditions of the Bernstein--von Mises theorem, the posterior variance agrees asymptotically with the frequentist variance. In finite samples, however, things are less clear. In this paper we explore this issue by first considering the frequentist properties (bias and variance) of the posterior mean in the important case of the normal location model, which consists of a single observation on a univariate Gaussian distribution with unknown mean and known variance. Based on these results, we derive new estimators of the frequentist bias and variance of the WALS estimator in finite samples. We then study the finite-sample performance of the proposed estimators by a Monte Carlo experiment with design derived from a real data application about the effect of abortion on crime rates.

An Econometric Learning Approach to Approximate Expectations in Empirical Macro Models

An Econometric Learning Approach to Approximate Expectations in Empirical Macro Models

Unemployment and econometric learning

We apply well-known results of the econometric learning literature to the Mortensen and Pissarides real business cycle model. Agents can always learn the unique rational expectations equilibrium (REE), for all possible well-defined sets of parameter values, by using the minimum-state-variable solution to the model and decreasing gain learning. From this perspective the assumption of rational expectations in the model could be seen as reasonable. But using a parametrisation with UK data, simulations show that the speed of convergence to the REE is slow. This type of learning dampens the cyclical response of unemployment to small structural shocks.

Unemployment and Econometric Learning

We apply well-known results of the econometric learning literature to the Mortensen-Pissarides real business cycle model. The unique rational expectations equilibrium (REE) is always expectationally stable with decreasing gain learning, and this result is robust to over-parametrisation of the econometric model relative to the minimum state variable form used by agents (Strong E-stability). And so, from this perspective, the assumption of rational expectations in the model is not unreasonable. However, using a parametrisation with UK data, simulations suggest that the implied rate of convergence to the REE with least squares learning is slow. The cyclical response of unemployment to structural shocks is muted under learning, and a parametrisation which guarantees root-t convergence is generally not consistent with attempts to match the observed volatility of labour market data using the standard model.

Stationarity of econometric learning with bounded memory and a predicted state variable

In this paper, we consider a model where producers set their prices based on their prediction of the aggregated price level and an exogenous variable, which can be a demand or a cost-push shock. To form their expectations, they use OLS-type econometric learning with bounded memory. We show that the aggregated price follows the random coefficient autoregressive process and we prove that this process is covariance stationary.

The Term Structure of Interest Rates and the Macroeconomy: Learning About Economic Dynamics from a FAVAR

Expectations about macroeconomic developments are important determinants of long term interest rates. In this paper, I compare two different assumptions on how agents may form their expectations about the economy and yields in a pseudo real time exercise. Based on the no-arbitrage factor-augmented vector autoregression model developed by Moench (2008), I apply a purely econometric learning scheme as proposed by Laubach, Tetlow, and Williams (2007) in the estimation and compare the results to those of an estimation without discounting. In- and out-of-sample performance indicates that the agents are more inclined to form their expectations according to the learning approach.

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Learning as a Rational Foundation for Macroeconomics and Finance

Expectations play a central role in modern macroeconomics. The econometric learning approach, in line with the cognitive consistency principle, models agents as forming expectations by estimating and updating subjective forecasting models in real time. This approach provides a stability test for RE equilibria and a selection criterion in models with multiple equilibria. Further features of learning, such as discounting of older data, use of misspecified models, or heterogeneous choice by agents between competing models, generate novel learning dynamics. Empirical applications are reviewed and the roles of the planning horizon and structural knowledge are discussed. We develop several applications of learning to macroeconomic policy: the scope of Ricardian equivalence, appropriate specification of interest-rate rules, implementation of price-level targeting to achieve learning-stability of the optimal RE equilibrium and whether under learning price-level targeting can rule out the deflation trap at the zero-lower-bound.

Learning and Macroeconomics

Expectations play a central role in modern macroeconomic theories. The econometric learning approach models economic agents as forming expectations by estimating and updating forecasting models in real time. The learning approach provides a stability test for rational expectations and a selection criterion in models with multiple equilibria. In addition, learning provides new dynamics if older data are discounted, if models are misspecified, or if agents choose between competing models. This paper describes the expectational stability (E-stability) principle and the stochastic approximation tools used to assess equilibria under learning. Applications of learning to a number of areas are reviewed, including the design of monetary and fiscal policy, business cycles, self-fulfilling prophecies, hyperinflation, liquidity traps, and asset prices.

Expectations, Learning and Monetary Policy: An Overview of Recent Research

Expectations about the future are central for determination of current macroeconomic outcomes and the formulation of monetary policy. Recent literature has explored ways for supplementing the benchmark of rational expectations with explicit models of expectations formation that rely on econometric learning. Some apparently natural policy rules turn out to imply expectational instability of private agents' learning. We use the standard New Keynesian model to illustrate this problem and survey the key results about interest-rate rules that deliver both uniqueness and stability of equilibrium under econometric learning. We then consider some practical concerns such as measurement errors in private expectations, observability of variables and learning of structural parameters required for policy. We also discuss some recent applications including policy design under perpetual learning, estimated models with learning, recurrent hyperinflations, and macroeconomic policy to combat liquidity traps and deflation.

Performance of monetary policy with internal central bank forecasting

Recent models of monetary policy have analyzed the desirability of different optimal and ad hoc interest rules under the restrictive assumption that forecasts of the private sector and the central bank are homogeneous. This paper studies the implications of heterogeneity in forecasting by the central bank and private agents for the performance of interest rules in a framework of econometric learning.

Stable Noisy K-state Markov Sunspots

We consider a linear stochastic univariate rational expectations model, with a predetermined variable, and consider solutions driven by an extraneous finite state Markov process as well as by the fundamental noise. We obtain conditions for existence of noisy k-state sunspot equilibria (noisy k-SSEs) and, for the case k=2, of noisy k-state dependent sunspot equilibria (noisy k-*SDSs). k-*SDSs are driven by a finite state sunspot but have an infinite range of values even in the nonstochastic model. Stability under econometric learning is analyzed using representations that nest both types of solution. For the case k=2, we find that noisy 2-SSEs and noisy 2-*SDSs are learnable for parameters in proper subsets of the regions of their existence.

Determinacy and Stability under Learning of Rational Expectations Equilibria

This paper studies relationships between the local determinacy of a stationary equilibrium in the perfect foresight dynamics, and its local stability in dynamics arising from econometric learning procedures. Attention is focused on linear scalar economies where agents forecast only one period ahead, and with an arbitrary, but fixed, number of predetermined variables. In such a framework, it is well known that there are no clear links between the determinacy of the stationary state in the perfect foresight dynamics on the levels of the state variable, and its stability under learning. The paper emphasizes, however, that this is not the right perfect foresight dynamics to look at whenever agents try to learn the coefficients of the perfect foresight dynamics restricted to an eigenspace of lower dimension. Indeed the paper introduces a growth rate perfect foresight dynamics on these coefficients and proves equivalence between determinacy in that dynamics and stability under learning provided that a simple sign condition is satisfied. Journal of Economic Literature Classification Numbers: E32, D83.

Learning, convergence, and stability with multiple rational expectations equilibria

For a linear model with multiple rational expectations equilibria (REE) we discuss the set of possible REE. Solutions include (i) locally unique minimal state variable solutions, taking an AR(1) form and (ii) continua of solutions which may depend on sunspots. We analyze the convergence of econometric learning to the different REE. There exist cases with more than one stable AR(1) solution. It is also possible for a continuum of solutions to be stable, but this property is not robust to overparametrization. An application is developed, and it is suggested that the exhibited phenomena may arise in applied macroeconomic models.

Rational Conjectures Equilibria in the Private Provision of Public Goods

This article examines the role of information acquisition and the interaction between learning and individual choices in a model of voluntary public good provision. It shows that if agents form conjectural variations via a simple econometric learning process, final equilibira are dependent upon initial conditions. There is a significant set of possible equilibria that arise as limit points of this process and they may be given a simple geometric interpretation.